But how the hell do you "believe in yourself"? That phrase is opaque to me.

I take it to mean something like "The time for a lucid appraisal of your own abilities is prior to action, not in the middle of it. Once you find yourself engaged in real-time application of some skill or other, act as if your mastery of that skill isn't at issue at all, rather than let yourself be distracted by assessments of the likelihood of failure, because they are likely to be self-fulfilling prophecies."

You can see why people prefer the short version.